基于曲率离散的几何非线性空间梁单元

Geometric Nonlinear Spatial Beam Elements With Curvature Interpolations

以绝对坐标为节点参数的梁单元在结构的几何非线性分析和多柔体系统动力学中都有广泛的应用前景.其中一种具有代表性的单元为基于精确几何模型的梁单元,但它的构造过程涉及对节点转动矢量的插值,由此引起了很多数值求解方面的困难.由Shabana提出的绝对坐标梁单元,其节点参数中不含转动矢量,从而避免了对转角的插值,但却为此大幅度地增加了节点参数.以大变形梁虚功率方程为理论基础,先通过单元的形心曲线插值得到端面曲率及其对弧长的变化率,进而对单元域内的曲率进行插值,提出了一种既可避免转动矢量插值同时又不增加节点参数的空间梁单元,可用于梁的大变形几何非线性分析.数值算例验证了该单元的合理性.

Beam elements with absolute nodal coordinates played an important role in the geometric nonlinear analysis of structures and dynamics of flexible multibody systems. O ne of such elements was the beam element based on the exact geometric beam model,in which the process of obtaining internal nodal forces involved interpolations of rotational angles,resulting in some numerical difficulties. Another such element proposed by Shabana,avoided the angular interpolations by replacing the nodal rotation parameters with many newly introduced nodal parameters. In accordance with the exact virtual power equations for beams with large deformations and the relationships between tangents of the beam centroid line and curvatures of the beam sections,a newspatial beam element with absolute nodal coordinates was presented. The nodal parameters of the presented element are the same with those of the element based on the exact geometric beam model,but the internal forces can be obtained without angular interpolations. N umerical examples verify its validity through comparison with the analytical results.